• Bulletin of the Korean Mathematical Society
• /
• v.56 no.6
• /
• pp.1467-1483
• /
• 2019

This paper analyzes a robust optimal reinsurance and investment strategy for an Ambiguity-Averse Insurer (AAI), who worries about model misspecification and insists on seeking robust optimal strategies. The AAI's surplus process is assumed to follow a jump-diffusion model, and he is allowed to purchase proportional reinsurance or acquire new business, meanwhile invest his surplus in a risk-free asset and a risky-asset, whose price is described by an Ornstein-Uhlenbeck process. Under the criterion for maximizing the expected exponential utility of terminal wealth, robust optimal strategy and value function are derived by applying the stochastic dynamic programming approach. Serval numerical examples are given to illustrate the impact of model parameters on the robust optimal strategies and the loss utility function from ignoring the model uncertainty.

• Proceedings of the KSME Conference
• /
• 2003.04a
• /
• pp.1254-1261
• /
• 2003

In this paper we present a simple and efficient robust optimal design formulation and its application to a resonant-type micro probe. The basic idea is to use the Gradient Index (GI) to improve robustness of the objective and constraint functions. In the robust optimal design procedure, a deterministic optimization for performance of MEMS structures is followed by design sensitivity analysis with respect to uncertainties such as fabrication errors and change of operating conditions. During the process of deterministic optimization and sensitivity analysis, dominant performance and uncertain variables are identified to define GI. The GI is incorporated as a term of objective and constraint functions in the robust optimal design formulation to make both performance and robustness improved. While most previous approaches for robust optimal design require statistical information on design variations, the proposed GI based method needs no such information and therefore is cost-efficient and easily applicable to early design stages. For the micro probe example, robust optimums are obtained to satisfy the targets for the measurement sensitivity and they are compared in terms of robustness and production yield with the deterministic optimums through the Monte Carlo simulation.

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• pp.73.5-73
• /
• 2001

In this paper, we present a procedure to design the robust optimal supervisor which has the minimal cost in the sense of average for a given multiple-modelled discrete event system DES. In order to design the robust optimal supervisor, we extend the optimal supervisor design algorithm for a deterministic DES to the case of multiple-modelled DESs. In addition, using the proposed algorithm with modified costs of events and penalities of states, we can show whether a robust supervisor for a given multiple-modelled DES exists and design the minimally restricted robust supervisor.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.27 no.7
• /
• pp.1234-1242
• /
• 2003

In this paper we present a simple and efficient robust optimal design formulation for MEMS structures and its application to a resonant-type micro probe. The basic idea is to use the gradient index (GI) to improve robustness of the objective and constraint functions. In the robust optimal design procedure, a deterministic optimization for performance of MEMS structures is followed by design sensitivity analysis with respect to uncertainties such as fabrication errors and change of operating conditions. During the process of deterministic optimization and sensitivity analysis, dominant performance and uncertain variables are identified to define GI. The GI is incorporated as a term of objective and constraint functions in the robust optimal design formulation to make both performance and robustness improved. While most previous approaches for robust optimal design require statistical information on design variations, the proposed GI based method needs no such information and therefore is cost-effective and easily applicable to early design stages. For the micro probe example, robust optimums are obtained to satisfy the targets for the measurement sensitivity and they are compared in terms of robustness and production yield with the deterministic optimums through the Monte Carlo simulation. This method, although shown for MEMS structures, may as well be easily applied to conventional mechanical structures where information on uncertainties is lacking but robustness is highly important.

• Journal of Institute of Control, Robotics and Systems
• /
• v.12 no.5
• /
• pp.411-418
• /
• 2006

There are mainly two types of bang-bang controllers for nominal linear time-invariant (LTI) system. Optimal bang-bang controller is designed based on optimal control theory and suboptimal bang-bang controller is obtained by using Lyapunov stability condition. In this paper, the suboptimal bang-bang control method is extended to LTI system involving both control input saturation and structured real parameter uncertainties by using Lyapunov robust stability condition. Two robust optimal bang-bang controllers are derived by minimizing the time derivative of Lyapunov function subjected to the limit of control input. The one is developed based on the classical quadratic stability(QS), and the other is developed based on the affine quadratic stability(AQS). And characteristics of the two controllers are compared. Especially, bounds of parameter uncertainties which theoretically guarantee robust stability of the two controllers are compared quantitatively for 1DOF vibrating system. Moreover, the validity of robust optimal bang-bang controller based on the AQS is shown through numerical simulations for this system.

• 제어로봇시스템학회:학술대회논문집
• /
• 2003.10a
• /
• pp.2004-2009
• /
• 2003

A robust optimal control design is proposed in this study for rigid robotic systems under the unknown load and the other uncertainties. The uncertainties are quadratically bounded for some positive definite matrix. Iterative method finding the Q weighting matrix is shown. Computer simulations have been done for a weight-lifting operation of a two-link manipulator and the result of the simulation shows that the proposed algorithm is very effective for a robust control of robotic systems.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2003.06a
• /
• pp.455-458
• /
• 2003

An optimal control approach to robust control design is proposed in this study for rigid robotic systems under the unknown load and the other uncertainties. The uncertainties are quadratically bounded for some positive definite matrix. Iterative method to find the matrix is shown. Simulations arc made for a weight-lifting operation of a two-link manipulator and the robust control performance of robotic systems by the proposed algorithm is remarkable.

• Journal of the Korean Society for Precision Engineering
• /
• v.20 no.12
• /
• pp.176-182
• /
• 2003

An optimal control approach to robust control design is proposed in this study for rigid robotic systems under the unknown load and the other uncertainties. The uncertainties are quadratically bounded for some positive definite matrix. Iterative method to find the matrix is shown. Simulations are made for a weight-lifting operation of a two-link manipulator and the robust control performance of robotic systems by the proposed algorithm is remarkable.

• Transactions of the Korean Society of Machine Tool Engineers
• /
• v.13 no.4
• /
• pp.79-86
• /
• 2004

Tooth errors inevitable in the manufacturing process have large effect on the strength/durability and vibration performances of gear drives. We show that the manufacturing errors affect the overall gear performances, especially vibration performance, and propose a robust optimal design method for gear dimension and its tooth flank form that guarantees reliable performances to the variation of manufacturing errors. This method begins with a search of optimal design candidates by using the previously developed gear optimal design method for the strength/durability and vibration performances. Then, the statistical analysis method is applied to find a robust design solution for the vibration performance which is generally very sensitive to the manufacturing variations.

• Journal of Institute of Control, Robotics and Systems
• /
• v.5 no.6
• /
• pp.656-666
• /
• 1999

In this paper, we design the optimal PD control system which has the robust performance. This PD control system is designed by applying genetic algorithm (GA) to the determination of proportional gain KP and derivative gain KD that are given by PD servo controller, to make the output of plant follow the output of reference model optimally. These proportional and derivatibe gains are simultaneously optimized in the search domain guaranteeing the robust performance of system. And, this PD control system is compared with $\mu$ -synthesis control system for the robust performance. The PD control system designed by the proposed method has not only the robust performance but also the better command tracking performance than that of the $\mu$ -synthesis control system. The effectiveness of this control system is verified by computer simulation.